The first Cobram Post Office opened on 1 January 1870 and was later renamed Boomerang and Cobram East. Cobram Post Office near its current location opened on 23 January 1888.
Cobram has one government high school and a primary school, an Anglican Prep-12 college, a Catholic primary school and a special developmental school. It also has a district hospital with emergency department and an associated nursing home for the elderly.
Cobram serves as the headquarters for the Shire of Moira, and forms part of the Central Ward. Three councillors are elected to represent Cobram and its surrounds, as are three for Numurkah and Nathalia and surrounds (West Ward), and three for Yarrawonga and surrounds (East Ward).
Smaller towns located nearby include Strathmerton, home of a large Kraft cheese processing plant, Yarroweyah, Katamatite, Katunga, Koonoomoo and the larger towns of Yarrawonga on the Victorian side and Tocumwal on the New South Wales side.
The Peaches & Cream Festival is held biennially around the Australia Day weekend in January.
Cobram is the birthplace of Murray Goulburn Co-operative, Australia's largest dairy co-operative, collecting 35% of Australia's milk produce through its numerous facilities throughout south eastern Australia. Murray Goulburn, along with the Meiji Dairy Corporation milk processing plant, a large abattoir and orange juice factories form the major industries of the town as well as serving as major employers.
V/Line once serviced Cobram with regular daily passenger trains as part of the Shepparton service. These train services were discontinued in 1993. Now V/Line operates multiple daily return connecting coach services between Cobram and Melbourne, as well as multiple return services to Albury and Mildura.
Cobram East is situated to the east of the town on the Murray Valley Highway, about a ten minute drive to Cobram.
Other popular sports played include basketball, table tennis, ballet, motorcross, netball, lawn tennis, badminton and lawn bowls. Cobram Bowling Club is centrally located and has three grass greens. The club has two ladies pennant teams and four Saturday pennant sides which participate in the Murray Bowls Association.
Cobram Station, built in 1907, is a large homestead located east of the town on the Murray Valley Highway. It is currently a private residence.
Around the region are numerous river beaches, with Thompson's Beach, claimed to be the largest inland beach in Australia located just north of Mookarii Street, before crossing into New South Wales.